For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
To find the length of the edge of the square base, we can use the Pythagorean theorem.
Let's assume the length of the edge of the square base is x.
Drawing a right triangle with one leg being half of the edge length (x/2), the height being 321 ft, and the hypotenuse being 436.5 ft, we have:
(x/2)^2 + 321^2 = 436.5^2
x^2/4 + 103041 = 190641.25
x^2/4 = 190641.25 - 103041
x^2/4 = 87600.25
x^2 = 350401
Taking the square root of both sides gives us:
x ≈ √350401
x ≈ 591.6
Rounding to the nearest tenth, the length of the edge of the square base is approximately 591.6 ft.
To find the length of r (the radius of the base of the pyramid), we can draw a right triangle where one leg is e/2 (half of the lateral edge length) and the hypotenuse is s (the slant height).
Using the Pythagorean theorem, we can solve for r:
r^2 + (e/2)^2 = s^2
r^2 + (25/2)^2 = 24^2
r^2 + 312.5 = 576
r^2 = 576 - 312.5
r^2 = 263.5
Taking the square root of both sides gives us:
r ≈ √263.5
r ≈ 16.24
Now that we have the radius of the base, we can use the Pythagorean theorem again to find the height of the pyramid (h).
Drawing another right triangle, where one leg is h, the hypotenuse is s, and the other leg is r, we have:
h^2 + r^2 = s^2
h^2 + 16.24^2 = 24^2
h^2 + 264.8976 = 576
h^2 = 576 - 264.8976
h^2 ≈ 311.1024
Taking the square root of both sides gives us:
h ≈ √311.1024
h ≈ 17.63
Rounding to the nearest whole number, the height of the pyramid is 18 inches.
wrong
I apologize for the mistake. Let's rework the problem:
To find the length of r, we can use the Pythagorean theorem in another right triangle, where one leg is e/2 and the hypotenuse is s:
r^2 + (e/2)^2 = s^2
r^2 + (25/2)^2 = 24^2
r^2 + 312.5 = 576
r^2 = 576 - 312.5
r^2 = 263.5
Taking the square root of both sides gives us:
r ≈ √263.5
r ≈ 16.2
Now, using the height (h) and the radius (r), we can use the Pythagorean theorem to solve for h:
h^2 + r^2 = s^2
h^2 + 16.2^2 = 24^2
h^2 + 262.44 = 576
h^2 = 576 - 262.44
h^2 ≈ 313.56
Taking the square root of both sides gives us:
h ≈ √313.56
h ≈ 17.7
Rounding to the nearest whole number, the height of the pyramid is 18 inches.
The Pyramid is an arena in Memphis, Tennessee. Its height is 321 ft., and its slant height is 436.5 ft. Find the length of the edge of the square base. Round the answer to the nearest tenth
A juice can is in the shape of a cylinder. It has a height of 122 mm and a diameter of 52 mm. What is the longest straw that can fit completely inside the juice can diagonally? Round the answer to the nearest tenth
To find the longest straw that can fit completely inside the juice can diagonally, we need to find the length of the diagonal of the cylinder.
The diagonal can be found by using the Pythagorean theorem with the height and diameter as the legs of a right triangle.
Let's assume the length of the diagonal is d.
Using the Pythagorean theorem, we have:
d^2 = h^2 + (diameter)^2
d^2 = 122^2 + 52^2
d^2 = 14884 + 2704
d^2 = 17588
Taking the square root of both sides gives us:
d ≈ √17588
d ≈ 132.6
Rounding to the nearest tenth, the longest straw that can fit completely inside the juice can diagonally is approximately 132.6 mm.